Regions of rationality: Maps for bounded agents Decision Analysis, in press

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Regions of rationality Maps for bounded
agents(Decision Analysis, in press)

• Robin M. Hogarth
• ICREA Universitat Pompeu Fabra, Barcelona
• Natalia Karelaia
• H.E.C., Université de Lausanne

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Regions of rationality

• The starting point
• heuristics and biases (Kahneman, Slovic,
  Tversky, 1982)
• simple decision rules can rival the predictive
  ability of complex algorithms (e.g., regression)
• (e.g., TTB Gigerenzer, Todd, the ABC Research
  Group, 1999 EW Dawes Corrigan,
  1974).
• Idea
• Attention as a scarce resource (Simon, 1978) -gt
• how much information to seek how to combine
  the pieces to make decisions in different
  regions
• identify decision rules that are appropriate to
  each region

• multiple-cue prediction (multi-attribute
  choice)
• cues are probabilistically related to the
  criterion

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A theoretical approach

• Effectiveness of several heuristics the
  probability that
• the best of m alternatives (with k cues) is
  identified
• the environmental conditions favoring various
  heuristics, e.g.
• differential weighting of cues
• inter-correlations of cues
• continuous/binary cues (c/b)
• noise in the environment
• interactions of these factors
• 2. Illustration 20 artificial and 4
  empirical environments

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Models

• Single Variable (SV) models
• Lexicographic SVc
• Lexicographic SVb
• DEBA (binary cues)
• Equal weight (EW) models
• 4. EWc
• 5. EWb
• Hybrid models
• 6. EW/DEBA
• EW/SVb
• Domran (DR) models (lower benchmark)
• 8. DRc
• DRb
• Multiple regression (MR) (upper benchmark)

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Method Single Variable, continuous cues - SVc

• Choosing between A B
• Y criterion and X cue
• Assume Y and X are N(0,1), gt0
• error, , N(0,
  ),
• Question

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Prob SVc chooses the best b/w A B
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Prob SVc chooses the best b/w A B
Therefore,
pdf probability density function
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Prob SVc chooses the best from A, B, C
- z1 and z2 are bivariate N
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SVc generalizing to the case of m alternatives
(mgt3)
(m-1) between-alternative comparisons
where
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Overall probability of correct choice by SVc

• Random sampling of m3 from the underlying
  population of alternatives.
• Either A, B, or C is chosen -gt overall
  probability is
• 3 P((XagtXb) (XagtXc))((YagtYb)(YagtYc))
  

integrated across
where , .
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Overall probability of correct choice by SVc
generalizing to mgt3
where
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Other models EWc MRc
Model
Error
Vd
di
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Models with binary cues - SVb
where
Therefore,
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Models with binary cues - SVb choosing 1 of 2
where
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Models with binary cues - DEBA Hybrids

• Prob a given alternative is chosen correctly
• the joint probability that the sequence of
  decisions (or eliminations) made at each stage is
  correct.
• Three key notions
• Appropriate model for each stage
• Partial correlations
• and partial st. deviations
• 3. Probability theory to calculate sequence of
  correct eliminations

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Illustration 20 artificial environments

• Choosing the best from 2, 3, and 4 alternatives
• n40

k
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Choosing the best from 3
Low inter-cue corr
High inter-cue corr
3 cues
3 cues
High inter-cue corr
Low inter-cue corr
5 cues
5 cues
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Some results

• (1) Similarity of models performance
• agreement between models (average between all
  pairs, A-D)63 (vs. 33.(3) of random
  agreement), lower when lower inter-cue corr.
• Model with continuous cues outperform their
  binary counterparts (except DR).
• DRb gt DRc.
• Choosing at random DRb in 51, DRc in 81.
• Larger inter-cue correlation reduces performance
  of all models (except SV).

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Regression of model performance
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Illustration 4 empirical datasets

• 1)  Golf all-around ranking, N60
• 1. Birdie average (-1)
• 2. Scoring average
• 3. Putting average
•  
•  
•  2) Golf earnings, N60
• 1. Top 10 finishes
• 2. All-around ranking (-1)
• 3. Consecutive cuts
•  
•  
• 3) PhD economics programs ratings-1993,
  http//www.phds.org, N107
•   1. of PhDs for the academic year 87-88 to
  91-92
• 2.  Total of program citations 88-92/ number
  program faculty
• 3. Faculty with research support
•  
•  

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Illustration empirical datasets
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Golf earnings
Golf ranking
Economics PhD programs
Consumer reports
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Discussion

• Our contributions
• Analytical analysis
• Regions of rationality a multidimensional
  terrain
• Further research implications
• Non-random sampling of alternatives
• Hybrids with categorical continuous variables
• Different loss functions
• Predicting consumer preferences
• Bounded rationality and expertise
• how do people build maps of their decision
  making terrain?